package breeze.optimize
/*
 Copyright 2015 David Hall, Daniel Ramage, Debasish Das

 Licensed under the Apache License, Version 2.0 (the "License")
 you may not use this file except in compliance with the License.
 You may obtain a copy of the License at

 http://www.apache.org/licenses/LICENSE-2.0

 Unless required by applicable law or agreed to in writing, software
 distributed under the License is distributed on an "AS IS" BASIS,
 WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 See the License for the specific language governing permissions and
 limitations under the License.
 */

import breeze.optimize.proximal.{ProjectL1, QuadraticMinimizer}
import org.scalatest._
import org.scalatest.funsuite._
import org.scalatest.propspec._
import org.scalatestplus.scalacheck._
import breeze.linalg._
import breeze.numerics._
import breeze.optimize.proximal.NonlinearMinimizer.Projection

import matchers.should.Matchers._

class ProjectedQuasiNewtonTest
    extends AnyPropSpec
    with ScalaCheckPropertyChecks
    with OptimizeTestBaseTrait
    with VectorMatchers
    {

  property("optimize a simple multivariate gaussian") {
    val optimizer = new ProjectedQuasiNewton(tolerance = 1.0E-9)
    forAll { (init: DenseVector[Double]) =>
      val f = new DiffFunction[DenseVector[Double]] {
        def calculate(x: DenseVector[Double]) = {
          (sum((x - 3.0) ^:^ 2.0), (x * 2.0) - 6.0)
        }
      }

      val result = optimizer.minimize(f, init)
      result should beSimilarTo(DenseVector.fill(result.size)(3.0), allowedDeviation = 1E-5)
    }
  }

  property("optimize a simple multivariate gaussian with projection") {
    val optimizer = new ProjectedQuasiNewton(tolerance = 1.0E-5, projection = _.map(scala.math.min(_, 2.0)))

    forAll { (init: DenseVector[Double]) =>
      init := clip(init, Double.NegativeInfinity, 2.0)
      val f = new DiffFunction[DenseVector[Double]] {
        def calculate(x: DenseVector[Double]) = {
          (sum((x - 3.0) ^:^ 4.0), ((x - 3.0) ^:^ 3.0) *:* 4.0)
        }
      }

      val result = optimizer.minimize(f, init)
      result should beSimilarTo(DenseVector.fill(result.size)(2.0), allowedDeviation = 1E-10)
    }
  }

  property("optimize a simple multivariate gaussian with l2 regularization") {
    val optimizer = new ProjectedQuasiNewton(tolerance = 1.0E-5)

    forAll { (init: DenseVector[Double]) =>
      val f = new DiffFunction[DenseVector[Double]] {
        def calculate(x: DenseVector[Double]) = {
          (norm((x - 3.0) ^:^ 2.0, 1), (x * 2.0) - 6.0)
        }
      }

      val targetValue = 3 / (1.0 / 2 + 1)
      val result = optimizer.minimize(DiffFunction.withL2Regularization(f, 1.0), init)
      result should beSimilarTo(
        DenseVector.ones[Double](init.size) * targetValue,
        allowedDeviation = 3E-3 * result.size)
    }
  }

  property("optimize a complicated function without projection") {
    val optimizer = new ProjectedQuasiNewton(tolerance = 1.0E-5)

    forAll { (a: DenseVector[Double]) =>
      val init = DenseVector.rand(a.size)
      val f = new DiffFunction[DenseVector[Double]] {
        def calculate(x: DenseVector[Double]) = {
          (sum(exp((x ^:^ 2.0) -:- (a *:* x))), (x * 2.0 -:- a) *:* exp((x ^:^ 2.0) -:- (a *:* x)))
        }
      }

      val result = optimizer.minimize(f, init)
      val minimum = f(a / 2.0)
      f(result) should be(minimum +- abs(minimum) * 1E-2)
    }
  }

  property("simple linear solve without projection") {
    val n = 5
    val H = new DenseMatrix(
      n,
      n,
      Array(1.8984250861699135, 0.5955576666769438, -1.484430453342902, -1.0434994471390804, -3.675310432634351,
        0.5955576666769438, 0.9090751938470876, -2.146380947361661, -0.13037609428980368, -0.40639564652095117,
        -1.484430453342902, -2.146380947361661, 10.262733520770384, -6.097698907163584, 2.29625304115155,
        -1.0434994471390804, -0.13037609428980368, -6.097698907163584, 27.775920405610677, -5.574220233644466,
        -3.675310432634351, -0.40639564652095117, 2.29625304115155, -5.574220233644466, 12.21329172136971)
    )
    val f = DenseVector(
      -1.2320199653150048,
      -0.14220655875869606,
      0.38477404739124765,
      -0.3480575854151014,
      -0.4729810900829228)

    val cost = QuadraticMinimizer.Cost(H, f * -1.0)
    val init = DenseVector.zeros[Double](n)

    init := 0.0
    val x = H \ f

    init := 0.0
    val nlResult = new ProjectedQuasiNewton().minimize(cost, init)
    assert(norm(x - nlResult, inf) < 1e-4)
  }

  property("simple linear solve with L1 projection compared to Octave") {
    val Hl1 = new DenseMatrix(
      25,
      25,
      Array(253.535098, 236.477785, 234.421906, 223.374867, 241.007512, 204.695511, 226.465507, 223.351032, 249.179386,
        221.411909, 238.679352, 203.579010, 217.564498, 243.852681, 266.607649, 213.994496, 241.620759, 223.602907,
        220.038678, 264.704959, 240.341716, 223.672378, 244.323303, 223.216217, 226.074990, 236.477785, 278.862035,
        245.756639, 237.489890, 252.783139, 214.077652, 241.816953, 238.790633, 260.536460, 228.121417, 255.103936,
        216.608405, 237.150426, 258.933231, 281.958112, 228.971242, 252.508513, 234.242638, 240.308477, 285.416390,
        254.792243, 240.176223, 259.048267, 235.566855, 236.277617, 234.421906, 245.756639, 269.162882, 231.416867,
        251.321527, 208.134322, 236.567647, 236.558029, 255.805108, 226.535825, 251.514713, 212.770208, 228.565362,
        261.748652, 273.946966, 227.411615, 252.767900, 232.823977, 233.084574, 278.315614, 250.872786, 235.227909,
        255.104263, 238.931093, 235.402356, 223.374867, 237.489890, 231.416867, 254.771963, 241.703229, 209.028084,
        231.517998, 228.768510, 250.805315, 216.548935, 245.473869, 207.687875, 222.036114, 250.906955, 263.018181,
        216.128966, 244.445283, 227.436840, 231.369510, 270.721492, 242.475130, 226.471530, 248.130112, 225.826557,
        228.266719, 241.007512, 252.783139, 251.321527, 241.703229, 285.702320, 219.051868, 249.442308, 240.400187,
        264.970407, 232.503138, 258.819837, 220.160683, 235.621356, 267.743972, 285.795029, 229.667231, 260.870105,
        240.751687, 247.183922, 289.044453, 260.715749, 244.210258, 267.159502, 242.992822, 244.070245, 204.695511,
        214.077652, 208.134322, 209.028084, 219.051868, 210.164224, 208.151908, 201.539036, 226.373834, 192.056565,
        219.950686, 191.459568, 195.982460, 226.739575, 240.677519, 196.116652, 217.352348, 203.533069, 204.581690,
        243.603643, 217.785986, 204.205559, 223.747953, 203.586842, 200.165867, 226.465507, 241.816953, 236.567647,
        231.517998, 249.442308, 208.151908, 264.007925, 227.080718, 253.174653, 220.322823, 248.619983, 210.100242,
        223.279198, 254.807401, 269.896959, 222.927882, 247.017507, 230.484479, 233.358639, 274.935489, 249.237737,
        235.229584, 253.029955, 228.601700, 230.512885, 223.351032, 238.790633, 236.558029, 228.768510, 240.400187,
        201.539036, 227.080718, 258.773479, 249.471480, 215.664539, 243.078577, 202.337063, 221.020998, 249.979759,
        263.356244, 213.470569, 246.182278, 225.727773, 229.873732, 266.295057, 242.954024, 225.510760, 249.370268,
        227.813265, 232.141964, 249.179386, 260.536460, 255.805108, 250.805315, 264.970407, 226.373834, 253.174653,
        249.471480, 302.360150, 237.902729, 265.769812, 224.947876, 243.088105, 273.690377, 291.076027, 241.089661,
        267.772651, 248.459822, 249.662698, 295.935799, 267.460908, 255.668926, 275.902272, 248.495606, 246.827505,
        221.411909, 228.121417, 226.535825, 216.548935, 232.503138, 192.056565, 220.322823, 215.664539, 237.902729,
        245.154567, 234.956316, 199.557862, 214.774631, 240.339217, 255.161923, 209.328714, 232.277540, 216.298768,
        220.296241, 253.817633, 237.638235, 220.785141, 239.098500, 220.583355, 218.962732, 238.679352, 255.103936,
        251.514713, 245.473869, 258.819837, 219.950686, 248.619983, 243.078577, 265.769812, 234.956316, 288.133073,
        225.087852, 239.810430, 268.406605, 283.289840, 233.858455, 258.306589, 240.263617, 246.844456, 290.492875,
        267.212598, 243.218596, 265.681905, 244.615890, 242.543363, 203.579010, 216.608405, 212.770208, 207.687875,
        220.160683, 191.459568, 210.100242, 202.337063, 224.947876, 199.557862, 225.087852, 217.501685, 197.897572,
        229.825316, 242.175607, 201.123644, 219.820165, 202.894307, 211.468055, 246.048907, 225.135194, 210.076305,
        226.806762, 212.014431, 205.123267, 217.564498, 237.150426, 228.565362, 222.036114, 235.621356, 195.982460,
        223.279198, 221.020998, 243.088105, 214.774631, 239.810430, 197.897572, 244.439113, 241.621129, 260.400953,
        216.482178, 236.805076, 216.680343, 223.816297, 263.188711, 236.311810, 222.950152, 244.636356, 219.121372,
        219.911078, 243.852681, 258.933231, 261.748652, 250.906955, 267.743972, 226.739575, 254.807401, 249.979759,
        273.690377, 240.339217, 268.406605, 229.825316, 241.621129, 302.928261, 288.344398, 238.549018, 267.239982,
        248.073140, 254.230916, 296.789984, 267.158551, 252.226496, 271.170860, 248.325354, 253.694013, 266.607649,
        281.958112, 273.946966, 263.018181, 285.795029, 240.677519, 269.896959, 263.356244, 291.076027, 255.161923,
        283.289840, 242.175607, 260.400953, 288.344398, 343.457361, 257.368309, 284.795470, 263.122266, 271.239770,
        320.209823, 283.933299, 264.416752, 292.035194, 268.764031, 265.345807, 213.994496, 228.971242, 227.411615,
        216.128966, 229.667231, 196.116652, 222.927882, 213.470569, 241.089661, 209.328714, 233.858455, 201.123644,
        216.482178, 238.549018, 257.368309, 239.295031, 234.913508, 218.066855, 219.648997, 257.969951, 231.243624,
        224.657569, 238.158714, 217.174368, 215.933866, 241.620759, 252.508513, 252.767900, 244.445283, 260.870105,
        217.352348, 247.017507, 246.182278, 267.772651, 232.277540, 258.306589, 219.820165, 236.805076, 267.239982,
        284.795470, 234.913508, 289.709239, 241.312315, 247.249491, 286.702147, 264.252852, 245.151647, 264.582984,
        240.842689, 245.837476, 223.602907, 234.242638, 232.823977, 227.436840, 240.751687, 203.533069, 230.484479,
        225.727773, 248.459822, 216.298768, 240.263617, 202.894307, 216.680343, 248.073140, 263.122266, 218.066855,
        241.312315, 255.363057, 230.209787, 271.091482, 239.220241, 225.387834, 247.486715, 226.052431, 224.119935,
        220.038678, 240.308477, 233.084574, 231.369510, 247.183922, 204.581690, 233.358639, 229.873732, 249.662698,
        220.296241, 246.844456, 211.468055, 223.816297, 254.230916, 271.239770, 219.648997, 247.249491, 230.209787,
        264.014907, 271.938970, 246.664305, 227.889045, 249.908085, 232.035369, 229.010298, 264.704959, 285.416390,
        278.315614, 270.721492, 289.044453, 243.603643, 274.935489, 266.295057, 295.935799, 253.817633, 290.492875,
        246.048907, 263.188711, 296.789984, 320.209823, 257.969951, 286.702147, 271.091482, 271.938970, 352.825726,
        286.200221, 267.716897, 297.182554, 269.776351, 266.721561, 240.341716, 254.792243, 250.872786, 242.475130,
        260.715749, 217.785986, 249.237737, 242.954024, 267.460908, 237.638235, 267.212598, 225.135194, 236.311810,
        267.158551, 283.933299, 231.243624, 264.252852, 239.220241, 246.664305, 286.200221, 294.042749, 246.504021,
        269.570596, 243.980697, 242.690997, 223.672378, 240.176223, 235.227909, 226.471530, 244.210258, 204.205559,
        235.229584, 225.510760, 255.668926, 220.785141, 243.218596, 210.076305, 222.950152, 252.226496, 264.416752,
        224.657569, 245.151647, 225.387834, 227.889045, 267.716897, 246.504021, 259.897656, 251.730847, 229.335712,
        229.759185, 244.323303, 259.048267, 255.104263, 248.130112, 267.159502, 223.747953, 253.029955, 249.370268,
        275.902272, 239.098500, 265.681905, 226.806762, 244.636356, 271.170860, 292.035194, 238.158714, 264.582984,
        247.486715, 249.908085, 297.182554, 269.570596, 251.730847, 303.872223, 251.585636, 247.878402, 223.216217,
        235.566855, 238.931093, 225.826557, 242.992822, 203.586842, 228.601700, 227.813265, 248.495606, 220.583355,
        244.615890, 212.014431, 219.121372, 248.325354, 268.764031, 217.174368, 240.842689, 226.052431, 232.035369,
        269.776351, 243.980697, 229.335712, 251.585636, 257.544914, 228.810942, 226.074990, 236.277617, 235.402356,
        228.266719, 244.070245, 200.165867, 230.512885, 232.141964, 246.827505, 218.962732, 242.543363, 205.123267,
        219.911078, 253.694013, 265.345807, 215.933866, 245.837476, 224.119935, 229.010298, 266.721561, 242.690997,
        229.759185, 247.878402, 228.810942, 253.353769)
    )
    val fl1 = DenseVector(-892.842851, -934.071560, -932.936015, -888.124343, -961.050207, -791.191087, -923.711397,
      -904.289301, -988.384984, -883.909133, -959.465030, -798.551172, -871.622303, -997.463289, -1043.912620,
      -863.013719, -976.975712, -897.033693, -898.694786, -1069.245497, -963.491924, -901.263474, -983.768031,
      -899.865392, -902.283567)
    val cost = QuadraticMinimizer.Cost(Hl1, fl1)

    val octaveL1 = DenseVector(0.18611, 0.00000, 0.06317, -0.10417, 0.11262, -0.20495, 0.52668, 0.32790, 0.19421,
      0.72180, 0.06309, -0.41326, -0.00000, 0.52078, -0.00000, 0.18040, 0.62915, 0.16329, -0.06424, 0.37539, 0.01659,
      0.00000, 0.11215, 0.24778, 0.04082)

    val s = octaveL1.foldLeft(0.0) { case (agg, entry) => agg + abs(entry) }
    val projection = Projection(ProjectL1(s))
    val pqnResult = new ProjectedQuasiNewton(projection = projection.project)
      .minimizeAndReturnState(cost, DenseVector.zeros[Double](25))

    println(s"L1 projection iter ${pqnResult.iter}")
    assert(norm(pqnResult.x - octaveL1, 2) < 1e-4)
  }
}
